薄膜厚度及折射率的计算方法
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‘‘Refractor’’ has several advantages: (1) it gives accurate results in a short time and reduces the number of arithmetic operations needed to compute n, k and d as compared to other computer techniques [1–4]; (2) it takes into account possible inhomogeneities in the film thickness; (3) it is not based on minimisation techniques as other commercial software; (4) using the obtained n, k and d values, the simulated spectrum as well as the experimental one can be graphically compared.
(1)
If the substrate refractive index is known, it is convenient to write this equation in terms of n(l) and x(l) = exp(Àad), the absorbance, where a = 4pk/l is the optical absorption coefficient of the thin film:
PACS: 07.05.Tp; 78.66.Bz; 78.20.Àc
Keywords: Transmittance; Refractive index; Extinction coefficient; Pulsed laser deposition
1. Introduction
The performance of planar optical devices depends on the wavelength dependence of the optical constants, i.e., the refractive index n(l) and the extinction coefficient k(l) of thin films, and their geometrical thickness, d. n(l), k(l) and d can be
2. Preliminary theoretical considerations
The considered optical system is a thin homogeneous film deposited on a weakly absorbing substrate (extinction coefficient ks % 0) with a thickness several orders of magnitude greater than that of the film and with a refractive index s. The substrate surfaces are considered smooth but not perfectly parallel so that interference effects due to the substrate are negligible. When a monochromatic light beam impinges perpendicularly on the surface covered with a thin film, multiple reflections occur at the interfaces of the system. Assuming that these reflections are coherent in the film and incoherent in the substrate, both the reflected and transmitted beams are subject to interference phenomena. The interference fringes can be used to determine the optical constants and thickness of the film. The procedure is as follows.
Taking into account all the multiple reflections at the three interfaces, the transmission T is a complex function of the variables l, n, k, s and d:
T ¼ Tðl; n; k; s; dÞ:
A.P. Caricato, A. Fazzi, G. Leggieri *
INFM, Dipartimento di Fisica, Universita` di Lecce, 73100 Lecce, Italy
Available online 30 March 2005
Abstract
A computer simulation program for processing transmission spectra of amorphous optical thin films deposited on weakly absorbing substrates and evaluation of the refractive index n, extinction coefficient k and thickness d was developed. The computer code is the implementation of an optical characterisation algorithm based on the determination of the upper and lower envelopes of the transmission spectrum interference fringes. Inhomogeneities in the thickness of the analysed films, which are responsible of a shrinking in the fringes amplitude, can be considered in the program. Relative errors in the calculated values of n, k and d have been determined using simulated transmission spectra in both cases of homogeneous and inhomogeneous films. The thickness and the refractive index of uniform films are calculated with an accuracy 0.5%, while the accuracy in the case including inhomogeneities is 2%. Simulation results for chalcogenide thin films deposited by pulsed laser deposition (PLD) on microscope slabs and glass slides are reported. # 2005 Elsevier B.V. All rights reserved.
The optical constants and thickness evaluated by ‘‘Refractor’’ for Pr3+-doped (2000 ppm) chalcogenide thin films, grown on microscope slabs and glass slides by PLD, are reported.
0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2005.03.069
A.P. Caricato et al. / Applied Surface Science 248 (2005) 440–445
T ¼ Tðn; xÞ:
For k2 ( n2, the expression for the transmittance can be written [7]:
Ax
TðlÞ ¼ B À Cx cos ’ þ Dx2
(2)
where A = 16n2s; B = (n + 1)3(n + s2); C = 2(n2 À 1) (n2 À s2); D = (n À 1)3(n À s2); w = 4pnd/l.
Since À1 cos w 1, T(l) values can vary
between
Tm
¼
Ax BþCxþDx2
and
TM
¼wenku.baidu.com
Ax BÀCxþDx2
.
A typical transmission spectrum at normal inci-
Applied Surface Science 248 (2005) 440–445
www.elsevier.com/locate/apsusc
A computer program for determination of thin films thickness and optical constants
* Corresponding author. Tel.: +39 0832 297479; fax: +39 0832 297505.
E-mail address: leggieri@le.infn.it (G. Leggieri).
calculated from the interference fringes present in the transmission, T(l), and reflection, R(l), spectra by using various techniques. Current methods for determining the optical constants of thin films are usually based on sophisticated computer iteration techniques [1–4]. A relatively simple method for the computation of the optical constants of dielectric films deposited on visible transparent substrates such as glass has been implemented by a computer program developed by us named ‘‘Refractor’’ and tested on optical films deposited by pulsed laser deposition
441
(PLD). The method is based on the determination of the upper and lower envelopes of the interference fringes in the measured transmission spectrum [5–7].
(1)
If the substrate refractive index is known, it is convenient to write this equation in terms of n(l) and x(l) = exp(Àad), the absorbance, where a = 4pk/l is the optical absorption coefficient of the thin film:
PACS: 07.05.Tp; 78.66.Bz; 78.20.Àc
Keywords: Transmittance; Refractive index; Extinction coefficient; Pulsed laser deposition
1. Introduction
The performance of planar optical devices depends on the wavelength dependence of the optical constants, i.e., the refractive index n(l) and the extinction coefficient k(l) of thin films, and their geometrical thickness, d. n(l), k(l) and d can be
2. Preliminary theoretical considerations
The considered optical system is a thin homogeneous film deposited on a weakly absorbing substrate (extinction coefficient ks % 0) with a thickness several orders of magnitude greater than that of the film and with a refractive index s. The substrate surfaces are considered smooth but not perfectly parallel so that interference effects due to the substrate are negligible. When a monochromatic light beam impinges perpendicularly on the surface covered with a thin film, multiple reflections occur at the interfaces of the system. Assuming that these reflections are coherent in the film and incoherent in the substrate, both the reflected and transmitted beams are subject to interference phenomena. The interference fringes can be used to determine the optical constants and thickness of the film. The procedure is as follows.
Taking into account all the multiple reflections at the three interfaces, the transmission T is a complex function of the variables l, n, k, s and d:
T ¼ Tðl; n; k; s; dÞ:
A.P. Caricato, A. Fazzi, G. Leggieri *
INFM, Dipartimento di Fisica, Universita` di Lecce, 73100 Lecce, Italy
Available online 30 March 2005
Abstract
A computer simulation program for processing transmission spectra of amorphous optical thin films deposited on weakly absorbing substrates and evaluation of the refractive index n, extinction coefficient k and thickness d was developed. The computer code is the implementation of an optical characterisation algorithm based on the determination of the upper and lower envelopes of the transmission spectrum interference fringes. Inhomogeneities in the thickness of the analysed films, which are responsible of a shrinking in the fringes amplitude, can be considered in the program. Relative errors in the calculated values of n, k and d have been determined using simulated transmission spectra in both cases of homogeneous and inhomogeneous films. The thickness and the refractive index of uniform films are calculated with an accuracy 0.5%, while the accuracy in the case including inhomogeneities is 2%. Simulation results for chalcogenide thin films deposited by pulsed laser deposition (PLD) on microscope slabs and glass slides are reported. # 2005 Elsevier B.V. All rights reserved.
The optical constants and thickness evaluated by ‘‘Refractor’’ for Pr3+-doped (2000 ppm) chalcogenide thin films, grown on microscope slabs and glass slides by PLD, are reported.
0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2005.03.069
A.P. Caricato et al. / Applied Surface Science 248 (2005) 440–445
T ¼ Tðn; xÞ:
For k2 ( n2, the expression for the transmittance can be written [7]:
Ax
TðlÞ ¼ B À Cx cos ’ þ Dx2
(2)
where A = 16n2s; B = (n + 1)3(n + s2); C = 2(n2 À 1) (n2 À s2); D = (n À 1)3(n À s2); w = 4pnd/l.
Since À1 cos w 1, T(l) values can vary
between
Tm
¼
Ax BþCxþDx2
and
TM
¼wenku.baidu.com
Ax BÀCxþDx2
.
A typical transmission spectrum at normal inci-
Applied Surface Science 248 (2005) 440–445
www.elsevier.com/locate/apsusc
A computer program for determination of thin films thickness and optical constants
* Corresponding author. Tel.: +39 0832 297479; fax: +39 0832 297505.
E-mail address: leggieri@le.infn.it (G. Leggieri).
calculated from the interference fringes present in the transmission, T(l), and reflection, R(l), spectra by using various techniques. Current methods for determining the optical constants of thin films are usually based on sophisticated computer iteration techniques [1–4]. A relatively simple method for the computation of the optical constants of dielectric films deposited on visible transparent substrates such as glass has been implemented by a computer program developed by us named ‘‘Refractor’’ and tested on optical films deposited by pulsed laser deposition
441
(PLD). The method is based on the determination of the upper and lower envelopes of the interference fringes in the measured transmission spectrum [5–7].